Question

A political polling agency wants to take a random sample of registered voters and ask whether or not they will vote for a certain candidate. One plan is to select 400 voters, another plan is to select 1,600 voters. If the study were conducted repeatedly (selecting different samples of people each time), which one of the following would be true regarding the resulting sample proportions of "yes" responses?

A. Different sample proportions would result each time, but for sample size 400 they would be centered (have their mean) at the true population proportion, whereas for sample size 1,600 they would not.
B. Different sample proportions would result each time, but for sample size 1,600 they would be centered (have their mean) at the true population proportion, whereas for sample size 400 they would not.
C. Different sample proportions would result each time, but for either sample size, they would be centered (have their mean) at the true population proportion.
D. For either sample size, using the same size each time, as long as the samples are drawn with replacement, they would be centered (have a mean) at 0.

Answer 1

C. Different sample proportions would result each time, but for either sample size, they would be centered (have their mean) at the true population proportion.

Explanation:

From the given information;

A political polling agency wants to take a random sample of registered voters and ask whether or not they will vote for a certain candidate.

A random sample is usually an outcome of any experiment that cannot be predicted before the result.

SO;

One plan is to select 400 voters, another plan is to select 1,600 voters

If the study were conducted repeatedly (selecting different samples of people each time);

Different sample proportions would result each time, but for either sample size, they would be centered (have their mean) at the true population proportion. This is because a sample proportion deals with random experiments that cannot be predicted in advance and they are quite known to be centered about the population proportion.